Paul:
Your system may actually be designed like that, and there may be a logical reason for it.
On my unit (a Coleman, not a Dometic) if the differential between the current room temperature and the thermostat setting is over 5 degrees, then both the heat strip and the furnace will come on until the differential falls to less than 5 degrees. Then the furnace goes off but the heat strip stays on until the room temp matches the thermostat setting. I think this is similar to many other unit brands. If your rig is at 70 degrees, try setting the thermostat to 72. Chances are the heat strip will come on alone. If you set the thermostat to 76 or greater chances are the heat strip and furnace will come on together.
You might not think the heat strip is working, because the air coming out doesn't feel hot. Ours feels like this too, and we have a 6000 btu heat strip on ours (yours is a 5600 btu unit) The difference between a small 1500w electric heater and the 1500w heat strip on the A/C unit is the volume of airflow, but they should put out the same btu's. If you have the heat strip on and watch the thermostat for a few minutes, you should see the temp rising. From what I understand the heat strip is generally not considered a primary heater, but only to give you a few degrees of heat....to take the chill off, so to speak.
When you think about it, running an electric heat strip off shore power rather than running the furnace off propane may save some money, and wear/tear on the furnace.
- Mike